Most will happen pretty quickly, but the longer you leave it, the more efficient it will be, because the reaction rate will slow as it nears completion.
I imagine polar migration should be quite fast at room temp or slightly higher temps with plenty of agitation. Its basically like stirring two soluble liquids together - doesnt take very long to become homogenized.
However, because alkaloids are generally somewhat soluble in both polar and nonpolar solvent (ie they dont precipitate out of nonpolar solvent when you remove a proton, they just become MORE soluble in a polar solvent than the nonpolar solvent they would already be in, in an A/B) there is a sort of uneven tug of war going on, where the water always wins...But it takes the water time to win every molecule...longer than mixing say water and vinegar, or water and food coloring for that matter. But I dont think it would take much longer. Just remember this- the more agitation and and higher temperature, the more thorough the reaction will be per given amount of time. If you let it sit on the counter for 4 hours, or you heat it in a water bath with constant agitation for 4 hrs, the latter will be far closer to 100% efficiency.
Exactly how long until you have say...98% completion? No idea. The above is all I could say. Maybe someone else knows some equations that will give you a rough reaction rate based on concentration.
Breaking down the cell wall with an acid however, will probably take much longer and would be much more profitable to do over a day or so with constant or occasional agitation and heat.
I prefer to lyse cell walls mechanically however. Soak your bark in water to get maximum turgor pressure (water pressure in cells via osmosis) for maybe a day. Then freeze/thaw it a couple times.
Because water is less dense as a solid than a liquid (a unique property), it expands as it freezes, and the sharp ice crystals have no problem slicing through the rigid cellulosic cell wall. Time wont matter with this. When its frozen its frozen. I do it twice.
